\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\Rightarrow\frac{a^3}{c^3}=\frac{b^3}{d^3}\)
áp dụng t/c dãy tỉ số bằng nhau ta có:
\(\frac{a^3}{c^3}=\frac{b^3}{d^3}=\frac{a^3+b^3}{c^3+d^3}\left(1\right)\)
\(\frac{a}{c}=\frac{b}{d}=\frac{a+b}{c+d}\Rightarrow\frac{a^3}{c^3}=\frac{\left(a+b\right)^3}{\left(c+d\right)^3}\left(2\right)\)
từ (1) và (2) => đpcm
\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}=\frac{a+b}{c+d}\)
\(\Rightarrow\frac{\left(a+b\right)^3}{\left(c+d\right)^3}=\frac{a^3}{c^3}=\frac{b^3}{d^3}=\frac{a^3+b^3}{c^3+d^3}\left(DPCM\right)\)
\(\frac{a}{b}\) = \(\frac{c}{d}\) \(\Rightarrow\) \(\frac{a}{c}\) =\(\frac{b}{d}\) \(\Rightarrow\) \(\frac{a^3}{c^3}\) = \(\frac{b^3}{d^3}\)
áp dụng t/c dãy tỉ số bằng nhau ta có :
\(\frac{a^3}{c^3}\) = \(\frac{b^3}{d^3}\) = \(\frac{a^{3^{ }}+b^3}{c^3+d^3}\) (1)
\(\frac{a}{c}\)= \(\frac{b}{d}\) =\(\frac{a+b}{c+d}\) \(\Rightarrow\) \(\frac{a^3}{c^3}\) = \(\frac{\left(a+b^{ }\right)^3}{\left(c+d\right)^3}\) ( 2 )
tứ (1) và (2) => đpcm